Loading Data

 [1] 8629 9627 4598 1031 4847 5189 9297 7081 5766 6406 5743 2069 5972 7935 4580
[16] 4154 7393 3193 5161 5851 1843 3540 1268 7823 4875 1574 4508

Recoding for effects and formating factors

HumanAf$ContextEffectf <-dplyr::recode(HumanAf$BuildingCategory_Building, 
                                      Residential = -0.5, Public= 0.5,
                                      .default = NaN)
HumanAf$AgentPresence <-dplyr::recode(HumanAf$AvatarPresenceCategory_Building,
                                             Omitted = -0.5, Present= 0.5,
                                             .default = NaN)
HumanAf$Agent_Action_level <-dplyr::recode(HumanAf$Agent_Action_level,
                                             Passive = -0.5, Active= 0.5,
                                             .default = NaN)
HumanAf$ContextEffectf <-factor(HumanAf$ContextEffectf,levels= c(-0.5, 0.5), 
                               labels=c('Residential', 'Public')) 
HumanAf$AgentPresencef <-factor(HumanAf$AgentPresence,
                                levels= c(-0.5, 0.5), 
                                labels=c('Omitted', 'Displayed'))
HumanAf$Agent_Action_levelf <-factor(HumanAf$Agent_Action_level,
                                levels= c(-0.5, 0.5), 
                                labels=c('Passive', 'Active'))

Data descriptives

MainVariables <- subset(HumanAf, select = c(AbsolutError_Building, RT_Building))
summary(MainVariables)
 AbsolutError_Building  RT_Building     
 Min.   :  0.00676     Min.   : 0.8616  
 1st Qu.: 13.31804     1st Qu.: 4.5096  
 Median : 34.42989     Median : 8.1352  
 Mean   : 48.03731     Mean   : 9.7420  
 3rd Qu.: 70.30188     3rd Qu.:13.7155  
 Max.   :179.97165     Max.   :29.7118  
 NA's   :8             NA's   :8        
summary(HumanAf$AgentPresence)
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max.      NA's 
-0.500000 -0.500000 -0.500000 -0.000823  0.500000  0.500000         8 
df = HumanAf[complete.cases(HumanAf),]
ggplot(df, aes(x=ContextEffectf,  y=AbsolutError_Building, fill=AgentPresencef)) + 
  geom_boxplot(notch=TRUE,
        notchwidth = 0.8,
        outlier.colour="red",
        outlier.fill="red",
        outlier.size=0.5)

ggplot(df, aes(x=ContextEffectf,  y=RT_Building, fill=AgentPresencef)) + 
  geom_boxplot(notch=TRUE,
        notchwidth = 0.8,
        outlier.colour="red",
        outlier.fill="red",
        outlier.size=0.5)

library(dplyr)
TwoFactorTable <- HumanAf %>% 
  group_by(ContextEffectf, AgentPresencef)%>%
  summarise(AccuracyMean = mean(AbsolutError_Building, na.rm = TRUE),
            n=n(),
            AccuracyStandardDev = sd(AbsolutError_Building, na.rm = TRUE),
            RT_BuildingMean = mean(RT_Building, na.rm = TRUE),
            RTStandardDev = sd(RT_Building, na.rm = TRUE))
`summarise()` has grouped output by 'ContextEffectf'. You can override using
the `.groups` argument.
library(tidyr)

Attaching package: 'tidyr'

The following objects are masked from 'package:Matrix':

    expand, pack, unpack

The following object is masked from 'package:dlookr':

    extract
TwoFactorTableUnite <- TwoFactorTable %>%
  unite("TwoFactor", ContextEffectf:AgentPresencef, sep= " ", remove = F)
  
TwoFactorTableUnite <-  TwoFactorTableUnite %>%
  mutate( AccuracyStandardError=AccuracyStandardDev/sqrt(n)) %>%  
  mutate( AccuracyStandardIC=AccuracyStandardDev * qt((1-0.05)/2 + .5, n-1)) %>%
  mutate( RTStandardError=RTStandardDev/sqrt(n)) 
Warning: Ignoring unknown aesthetics: linetype

Warning: Ignoring unknown aesthetics: linetype

library(dplyr)
ThreeFactorTable <- HumanAf %>% 
  group_by(ContextEffectf, AgentPresencef, Agent_Action_levelf)%>%
  summarise(AccuracyMean = mean(AbsolutError_Building, na.rm = TRUE),
            n=n(),
            AccuracyStandardDev = sd(AbsolutError_Building, na.rm = TRUE),
            RT_BuildingMean = mean(RT_Building, na.rm = TRUE),
            RTStandardDev = sd(RT_Building, na.rm = TRUE))
`summarise()` has grouped output by 'ContextEffectf', 'AgentPresencef'. You can
override using the `.groups` argument.
library(tidyr)
ThreeFactorTableUnite <- ThreeFactorTable %>%
  unite("ThreeFactor", ContextEffectf:AgentPresencef, sep= " ", remove = F)
  
ThreeFactorTableUnite <-  ThreeFactorTableUnite %>%
  mutate( AccuracyStandardError=AccuracyStandardDev/sqrt(n)) %>%  
  mutate( AccuracyStandardIC=AccuracyStandardDev * qt((1-0.05)/2 + .5, n-1)) %>%
  mutate( RTStandardError=RTStandardDev/sqrt(n)) 
ThreeFactorTableUnite <-ThreeFactorTableUnite  %>% drop_na()
Warning: Ignoring unknown aesthetics: linetype

Warning: Ignoring unknown aesthetics: linetype

Checking for the distribution of Absolut error

df$AbsolutError_BuildingR <- round(df$AbsolutError_Building, digits = 3)
qqp(df$AbsolutError_BuildingR, "norm")

[1] 1283  318
n_distinct(df$ID)
[1] 17
# Set up contrast to sum zero A.K.A compare each level equally
contrasts(df$ContextEffectf) <- "contr.sum"
contrasts(df$AgentPresencef) <- "contr.sum"
contrasts(df$Agent_Action_levelf) <- "contr.sum"

Linear mixed models

Assessing the need for a multilevel model

interceptOnly <-gls(AbsolutError_Building ~ 1, data = df, 
                    method = "ML")
IDrandomInterceptOnly <-lme(AbsolutError_Building ~ 1, data = df,  
                            random =~1|ID,
                            method = "ML")
StartlocationsrandomIntercept <-update(IDrandomInterceptOnly, .~.,   
                              random=~1|ID/PointingTaskStartingLocations_Building,
                              method= "ML")

Including Id and starting position as random effects significantly improves the fit of the model

Absolut Error Models

I am adding one main factor at a time

Just agent category

AgentActive <-update(StartlocationsrandomIntercept, .~. + Agent_Action_levelf)
summary(AgentActive)
Linear mixed-effects model fit by maximum likelihood
  Data: df 
       AIC      BIC    logLik
  39223.21 39254.43 -19606.61

Random effects:
 Formula: ~1 | ID
        (Intercept)
StdDev:    12.44818

 Formula: ~1 | PointingTaskStartingLocations_Building %in% ID
        (Intercept) Residual
StdDev:     13.8596 40.00401

Fixed effects:  AbsolutError_Building ~ Agent_Action_levelf 
                        Value Std.Error   DF   t-value p-value
(Intercept)          47.89518 3.1537650 3326 15.186666       0
Agent_Action_levelf1  2.87219 0.6743963 3326  4.258904       0
 Correlation: 
                     (Intr)
Agent_Action_levelf1 -0.012

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max 
-2.0857630 -0.6696041 -0.2240354  0.4811421  3.4992164 

Number of Observations: 3803
Number of Groups: 
                                            ID 
                                            17 
PointingTaskStartingLocations_Building %in% ID 
                                           476 
Anova(AgentActive, test.statistic="F", type=3)
Analysis of Deviance Table (Type III tests)

Response: AbsolutError_Building
                      Chisq Df Pr(>Chisq)    
(Intercept)         230.756  1  < 2.2e-16 ***
Agent_Action_levelf  18.148  1  2.044e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Agent category and location category

MeaningfulContext <-update(AgentActive, .~. + ContextEffectf)
summary(MeaningfulContext)
Linear mixed-effects model fit by maximum likelihood
  Data: df 
       AIC     BIC    logLik
  39215.44 39252.9 -19601.72

Random effects:
 Formula: ~1 | ID
        (Intercept)
StdDev:    12.44457

 Formula: ~1 | PointingTaskStartingLocations_Building %in% ID
        (Intercept) Residual
StdDev:    13.98064 39.92712

Fixed effects:  AbsolutError_Building ~ Agent_Action_levelf + ContextEffectf 
                        Value Std.Error   DF   t-value p-value
(Intercept)          47.89901 3.1542071 3325 15.185754  0.0000
Agent_Action_levelf1  2.80568 0.6737912 3325  4.164014  0.0000
ContextEffectf1       2.10977 0.6740993 3325  3.129760  0.0018
 Correlation: 
                     (Intr) Ag_A_1
Agent_Action_levelf1 -0.012       
ContextEffectf1       0.000 -0.031

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max 
-2.0354326 -0.6646727 -0.2213412  0.4817722  3.5492386 

Number of Observations: 3803
Number of Groups: 
                                            ID 
                                            17 
PointingTaskStartingLocations_Building %in% ID 
                                           476 
Anova(MeaningfulContext, test.statistic="F", type=3)
Analysis of Deviance Table (Type III tests)

Response: AbsolutError_Building
                       Chisq Df Pr(>Chisq)    
(Intercept)         230.7892  1  < 2.2e-16 ***
Agent_Action_levelf  17.3527  1  3.105e-05 ***
ContextEffectf        9.8031  1   0.001742 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Agent and location interaction

TwofactorInteraction <-update(StartlocationsrandomIntercept, .~. + ContextEffectf*Agent_Action_levelf)
summary(TwofactorInteraction)
Linear mixed-effects model fit by maximum likelihood
  Data: df 
       AIC      BIC    logLik
  39212.75 39256.46 -19599.38

Random effects:
 Formula: ~1 | ID
        (Intercept)
StdDev:    12.42152

 Formula: ~1 | PointingTaskStartingLocations_Building %in% ID
        (Intercept) Residual
StdDev:    13.93913 39.90874

Fixed effects:  AbsolutError_Building ~ ContextEffectf + Agent_Action_levelf +      ContextEffectf:Agent_Action_levelf 
                                        Value Std.Error   DF   t-value p-value
(Intercept)                          47.85124 3.1488977 3324 15.196188  0.0000
ContextEffectf1                       2.02550 0.6749036 3324  3.001174  0.0027
Agent_Action_levelf1                  2.80973 0.6735061 3324  4.171793  0.0000
ContextEffectf1:Agent_Action_levelf1  1.46554 0.6768591 3324  2.165205  0.0304
 Correlation: 
                                     (Intr) CntxE1 Ag_A_1
ContextEffectf1                       0.001              
Agent_Action_levelf1                 -0.012 -0.031       
ContextEffectf1:Agent_Action_levelf1 -0.007 -0.057  0.003

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max 
-2.0133937 -0.6586408 -0.2297155  0.4871098  3.5268823 

Number of Observations: 3803
Number of Groups: 
                                            ID 
                                            17 
PointingTaskStartingLocations_Building %in% ID 
                                           476 
Anova(TwofactorInteraction)
Analysis of Deviance Table (Type II tests)

Response: AbsolutError_Building
                                     Chisq Df Pr(>Chisq)    
ContextEffectf                      9.8047  1   0.001741 ** 
Agent_Action_levelf                17.3754  1  3.068e-05 ***
ContextEffectf:Agent_Action_levelf  4.6930  1   0.030285 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise<- emmeans(TwofactorInteraction, pairwise ~ ContextEffectf*Agent_Action_levelf)
Warning: contrasts dropped from factor ContextEffectf
Warning: contrasts dropped from factor Agent_Action_levelf
Pairwise
$emmeans
 ContextEffectf Agent_Action_levelf emmean   SE df lower.CL upper.CL
 Residential    Passive               54.2 3.34 16     47.1     61.2
 Public         Passive               47.2 3.35 16     40.1     54.3
 Residential    Active                45.6 3.38 16     38.4     52.8
 Public         Active                44.5 3.36 16     37.3     51.6

Degrees-of-freedom method: containment 
Confidence level used: 0.95 

$contrasts
 contrast                                 estimate   SE   df t.ratio p.value
 Residential Passive - Public Passive         6.98 1.86 3324   3.761  0.0010
 Residential Passive - Residential Active     8.55 1.91 3324   4.472  <.0001
 Residential Passive - Public Active          9.67 1.88 3324   5.152  <.0001
 Public Passive - Residential Active          1.57 1.94 3324   0.810  0.8498
 Public Passive - Public Active               2.69 1.91 3324   1.410  0.4934
 Residential Active - Public Active           1.12 1.97 3324   0.570  0.9411

Degrees-of-freedom method: containment 
P value adjustment: tukey method for comparing a family of 4 estimates 
plot(Pairwise[[2]], CIs = TRUE)

### Interaction plus presence

AgentPresence <-update(TwofactorInteraction, .~. + AgentPresencef)
summary(AgentPresence)
Linear mixed-effects model fit by maximum likelihood
  Data: df 
       AIC      BIC   logLik
  39214.41 39264.36 -19599.2

Random effects:
 Formula: ~1 | ID
        (Intercept)
StdDev:    12.42074

 Formula: ~1 | PointingTaskStartingLocations_Building %in% ID
        (Intercept) Residual
StdDev:      13.943 39.90611

Fixed effects:  AbsolutError_Building ~ ContextEffectf + Agent_Action_levelf +      AgentPresencef + ContextEffectf:Agent_Action_levelf 
                                        Value Std.Error   DF   t-value p-value
(Intercept)                          47.85089 3.1491576 3323 15.194823  0.0000
ContextEffectf1                       2.03191 0.6750415 3323  3.010048  0.0026
Agent_Action_levelf1                  2.80812 0.6735646 3323  4.169040  0.0000
AgentPresencef1                       0.39558 0.6729468 3323  0.587831  0.5567
ContextEffectf1:Agent_Action_levelf1  1.46725 0.6769202 3323  2.167540  0.0303
 Correlation: 
                                     (Intr) CntxE1 Ag_A_1 AgntP1
ContextEffectf1                       0.001                     
Agent_Action_levelf1                 -0.012 -0.031              
AgentPresencef1                       0.000  0.016 -0.004       
ContextEffectf1:Agent_Action_levelf1 -0.007 -0.057  0.003  0.004

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max 
-2.0211553 -0.6600032 -0.2313468  0.4854995  3.5160738 

Number of Observations: 3803
Number of Groups: 
                                            ID 
                                            17 
PointingTaskStartingLocations_Building %in% ID 
                                           476 
Anova(AgentPresence)
Analysis of Deviance Table (Type II tests)

Response: AbsolutError_Building
                                     Chisq Df Pr(>Chisq)    
ContextEffectf                      9.8628  1   0.001687 ** 
Agent_Action_levelf                17.3573  1  3.097e-05 ***
AgentPresencef                      0.3460  1   0.556386    
ContextEffectf:Agent_Action_levelf  4.7044  1   0.030085 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Three way interactions

AllInteractions <-update(StartlocationsrandomIntercept, .~. + ContextEffectf*Agent_Action_levelf*AgentPresencef)
summary(AllInteractions)
Linear mixed-effects model fit by maximum likelihood
  Data: df 
       AIC      BIC    logLik
  39219.49 39288.17 -19598.75

Random effects:
 Formula: ~1 | ID
        (Intercept)
StdDev:    12.41768

 Formula: ~1 | PointingTaskStartingLocations_Building %in% ID
        (Intercept) Residual
StdDev:    13.97801 39.89464

Fixed effects:  AbsolutError_Building ~ ContextEffectf + Agent_Action_levelf +      AgentPresencef + ContextEffectf:Agent_Action_levelf + ContextEffectf:AgentPresencef +      Agent_Action_levelf:AgentPresencef + ContextEffectf:Agent_Action_levelf:AgentPresencef 
                                                        Value Std.Error   DF
(Intercept)                                          47.86050 3.1499994 3320
ContextEffectf1                                       2.03156 0.6752019 3320
Agent_Action_levelf1                                  2.80414 0.6737584 3320
AgentPresencef1                                       0.41528 0.6745097 3320
ContextEffectf1:Agent_Action_levelf1                  1.46168 0.6771464 3320
ContextEffectf1:AgentPresencef1                       0.55511 0.6744019 3320
Agent_Action_levelf1:AgentPresencef1                 -0.09960 0.6734941 3320
ContextEffectf1:Agent_Action_levelf1:AgentPresencef1 -0.34613 0.6729880 3320
                                                       t-value p-value
(Intercept)                                          15.193812  0.0000
ContextEffectf1                                       3.008819  0.0026
Agent_Action_levelf1                                  4.161942  0.0000
AgentPresencef1                                       0.615674  0.5382
ContextEffectf1:Agent_Action_levelf1                  2.158591  0.0310
ContextEffectf1:AgentPresencef1                       0.823109  0.4105
Agent_Action_levelf1:AgentPresencef1                 -0.147891  0.8824
ContextEffectf1:Agent_Action_levelf1:AgentPresencef1 -0.514325  0.6071
 Correlation: 
                                                     (Intr) CntxE1 Ag_A_1
ContextEffectf1                                       0.001              
Agent_Action_levelf1                                 -0.012 -0.031       
AgentPresencef1                                       0.000  0.016 -0.005
ContextEffectf1:Agent_Action_levelf1                 -0.007 -0.057  0.003
ContextEffectf1:AgentPresencef1                       0.003 -0.004  0.000
Agent_Action_levelf1:AgentPresencef1                 -0.001  0.000  0.005
ContextEffectf1:Agent_Action_levelf1:AgentPresencef1  0.000 -0.003  0.011
                                                     AgntP1 CnE1:A_A_1 CE1:AP
ContextEffectf1                                                              
Agent_Action_levelf1                                                         
AgentPresencef1                                                              
ContextEffectf1:Agent_Action_levelf1                  0.004                  
ContextEffectf1:AgentPresencef1                       0.010 -0.004           
Agent_Action_levelf1:AgentPresencef1                 -0.057  0.013     -0.028
ContextEffectf1:Agent_Action_levelf1:AgentPresencef1 -0.030  0.006     -0.056
                                                     A_A_1:
ContextEffectf1                                            
Agent_Action_levelf1                                       
AgentPresencef1                                            
ContextEffectf1:Agent_Action_levelf1                       
ContextEffectf1:AgentPresencef1                            
Agent_Action_levelf1:AgentPresencef1                       
ContextEffectf1:Agent_Action_levelf1:AgentPresencef1  0.005

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max 
-2.0176639 -0.6583698 -0.2275608  0.4864835  3.5361017 

Number of Observations: 3803
Number of Groups: 
                                            ID 
                                            17 
PointingTaskStartingLocations_Building %in% ID 
                                           476 
Anova(AllInteractions)
Analysis of Deviance Table (Type II tests)

Response: AbsolutError_Building
                                                    Chisq Df Pr(>Chisq)    
ContextEffectf                                     9.8763  1   0.001674 ** 
Agent_Action_levelf                               17.3669  1  3.081e-05 ***
AgentPresencef                                     0.3465  1   0.556122    
ContextEffectf:Agent_Action_levelf                 4.6823  1   0.030474 *  
ContextEffectf:AgentPresencef                      0.6340  1   0.425877    
Agent_Action_levelf:AgentPresencef                 0.0212  1   0.884364    
ContextEffectf:Agent_Action_levelf:AgentPresencef  0.2651  1   0.606646    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model selections, most likely we will keep Two factor interaction plus presence

anova(interceptOnly, IDrandomInterceptOnly, StartlocationsrandomIntercept, 
       AgentActive, MeaningfulContext, TwofactorInteraction, AgentPresence)
                              Model df      AIC      BIC    logLik   Test
interceptOnly                     1  2 39616.63 39629.12 -19806.31       
IDrandomInterceptOnly             2  3 39345.03 39363.76 -19669.51 1 vs 2
StartlocationsrandomIntercept     3  4 39239.31 39264.29 -19615.66 2 vs 3
AgentActive                       4  5 39223.21 39254.43 -19606.60 3 vs 4
MeaningfulContext                 5  6 39215.44 39252.90 -19601.72 4 vs 5
TwofactorInteraction              6  7 39212.75 39256.46 -19599.38 5 vs 6
AgentPresence                     7  8 39214.41 39264.36 -19599.20 6 vs 7
                                L.Ratio p-value
interceptOnly                                  
IDrandomInterceptOnly         273.60305  <.0001
StartlocationsrandomIntercept 107.71327  <.0001
AgentActive                    18.10324  <.0001
MeaningfulContext               9.76860  0.0018
TwofactorInteraction            4.68893  0.0304
AgentPresence                   0.34596  0.5564

Standardized residuals of the models

plot(TwofactorInteraction, which = 1)

plot(MeaningfulContext, which = 1)

### General linear models using a log link link function on an assumed gaussian distribution

GHQ <- glmer(AbsolutError_Building ~  ContextEffectf*AgentPresencef + (1|ID), data = HumanAf,family=gaussian(link = "log"), nAGQ = 25)  
Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
 - Rescale variables?
summary(GHQ)
Generalized linear mixed model fit by maximum likelihood (Adaptive
  Gauss-Hermite Quadrature, nAGQ = 25) [glmerMod]
 Family: gaussian  ( log )
Formula: AbsolutError_Building ~ ContextEffectf * AgentPresencef + (1 |  
    ID)
   Data: HumanAf

     AIC      BIC   logLik deviance df.resid 
 7608606  7608644 -3804297  7608594     4245 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.6833 -0.7199 -0.2728  0.4820  3.3811 

Random effects:
 Groups   Name        Variance Std.Dev.
 ID       (Intercept)  128.8   11.35   
 Residual             1789.8   42.31   
Number of obs: 4251, groups:  ID, 19

Fixed effects:
                                               Estimate Std. Error t value
(Intercept)                                   3.8702587  0.0615479  62.882
ContextEffectfPublic                         -0.0634144  0.0008766 -72.341
AgentPresencefDisplayed                       0.0035992  0.0008493   4.238
ContextEffectfPublic:AgentPresencefDisplayed -0.0163270  0.0012462 -13.102
                                             Pr(>|z|)    
(Intercept)                                   < 2e-16 ***
ContextEffectfPublic                          < 2e-16 ***
AgentPresencefDisplayed                      2.26e-05 ***
ContextEffectfPublic:AgentPresencefDisplayed  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) CntxEP AgntPD
CntxtEffctP -0.007              
AgntPrsncfD -0.007  0.491       
CntxtEP:APD  0.005 -0.705 -0.683
optimizer (Nelder_Mead) convergence code: 0 (OK)
Model is nearly unidentifiable: very large eigenvalue
 - Rescale variables?
Anova(GHQ)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: AbsolutError_Building
                                  Chisq Df Pr(>Chisq)    
ContextEffectf                13247.445  1  < 2.2e-16 ***
AgentPresencef                   41.748  1  1.038e-10 ***
ContextEffectf:AgentPresencef   171.656  1  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(GHQ)
Analysis of Variance Table
                              npar  Sum Sq Mean Sq F value
ContextEffectf                   1 13283.6 13283.6  7.4219
AgentPresencef                   1    41.6    41.6  0.0233
ContextEffectf:AgentPresencef    1   172.0   172.0  0.0961
emmeans(GHQ, pairwise ~ ContextEffectf:AgentPresencef, type = "response")
$emmeans
 ContextEffectf AgentPresencef response   SE  df asymp.LCL asymp.UCL
 Residential    Omitted            48.0 2.95 Inf      42.5      54.1
 Public         Omitted            45.0 2.77 Inf      39.9      50.8
 Residential    Displayed          48.1 2.96 Inf      42.7      54.3
 Public         Displayed          44.4 2.74 Inf      39.4      50.1

Confidence level used: 0.95 
Intervals are back-transformed from the log scale 

$contrasts
 contrast                                     ratio        SE  df null z.ratio
 Residential Omitted / Public Omitted        1.0655 0.0009340 Inf    1  72.341
 Residential Omitted / Residential Displayed 0.9964 0.0008462 Inf    1  -4.238
 Residential Omitted / Public Displayed      1.0791 0.0009567 Inf    1  85.886
 Public Omitted / Residential Displayed      0.9352 0.0008145 Inf    1 -76.942
 Public Omitted / Public Displayed           1.0128 0.0009213 Inf    1  13.991
 Residential Displayed / Public Displayed    1.0830 0.0009566 Inf    1  90.276
 p.value
  <.0001
  0.0001
  <.0001
  <.0001
  <.0001
  <.0001

P value adjustment: tukey method for comparing a family of 4 estimates 
Tests are performed on the log scale

Response Time models

Checking for the distribution of RT

df = HumanAf[complete.cases(HumanAf),]
df$RTr <- round(df$RT_Building, digits = 3)
qqp(df$RT_Building, "norm")

[1] 1132 1277
qqp(df$RT_Building, "lnorm")

[1] 1132 1277
interceptOnlyt <-gls(log(RTr) ~ 1, data = df, 
                    method = "ML")
IDrandomInterceptOnlyt <-lme(log(RTr) ~ 1, data = df,  
                            random =~1|ID,
                            method = "ML")
StartlocationsrandomInterceptt <-lme(log(RTr) ~ 1, data = df,   
                              random=~1|ID|PointingTaskStartingLocations_Building,
                              method= "ML")
MeaningfulContext <-update(StartlocationsrandomInterceptt, .~. + ContextEffectf)
AgentActive <-update(StartlocationsrandomIntercept, .~. + Agent_Action_levelf)
TwofactorInteraction <-update(StartlocationsrandomIntercept, .~. + ContextEffectf*Agent_Action_levelf)
summary(TwofactorInteraction)
Linear mixed-effects model fit by maximum likelihood
  Data: df 
       AIC      BIC    logLik
  12983.92 13027.63 -6484.962

Random effects:
 Formula: ~1 | ID
        (Intercept)
StdDev:   0.3522174

 Formula: ~1 | PointingTaskStartingLocations_Building %in% ID
        (Intercept) Residual
StdDev:   0.3469856  1.28678

Fixed effects:  log(AbsolutError_Building) ~ ContextEffectf + Agent_Action_levelf +      ContextEffectf:Agent_Action_levelf 
                                                   Value  Std.Error   DF
(Intercept)                                     3.429675 0.09606976 3324
ContextEffectfPublic                           -0.245529 0.05923021 3324
Agent_Action_levelfActive                      -0.222284 0.06103493 3324
ContextEffectfPublic:Agent_Action_levelfActive  0.219906 0.08637019 3324
                                                t-value p-value
(Intercept)                                    35.69984  0.0000
ContextEffectfPublic                           -4.14533  0.0000
Agent_Action_levelfActive                      -3.64192  0.0003
ContextEffectfPublic:Agent_Action_levelfActive  2.54609  0.0109
 Correlation: 
                                               (Intr) CntxEP Ag_A_A
ContextEffectfPublic                           -0.299              
Agent_Action_levelfActive                      -0.289  0.472       
ContextEffectfPublic:Agent_Action_levelfActive  0.205 -0.688 -0.709

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max 
-6.0999775 -0.4666124  0.1969789  0.6806818  2.0367120 

Number of Observations: 3803
Number of Groups: 
                                            ID 
                                            17 
PointingTaskStartingLocations_Building %in% ID 
                                           476 
Anova(TwofactorInteraction)
Analysis of Deviance Table (Type II tests)

Response: log(AbsolutError_Building)
                                     Chisq Df Pr(>Chisq)    
ContextEffectf                     10.8884  1  0.0009677 ***
Agent_Action_levelf                 6.7910  1  0.0091617 ** 
ContextEffectf:Agent_Action_levelf  6.4894  1  0.0108520 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
AgentPresence <-update(TwofactorInteraction, .~. + AgentPresencef)
summary(AgentPresence)
Linear mixed-effects model fit by maximum likelihood
  Data: df 
       AIC      BIC    logLik
  12985.85 13035.79 -6484.923

Random effects:
 Formula: ~1 | ID
        (Intercept)
StdDev:   0.3522327

 Formula: ~1 | PointingTaskStartingLocations_Building %in% ID
        (Intercept) Residual
StdDev:   0.3469344 1.286775

Fixed effects:  log(AbsolutError_Building) ~ ContextEffectf + Agent_Action_levelf +      AgentPresencef + ContextEffectf:Agent_Action_levelf 
                                                   Value  Std.Error   DF
(Intercept)                                     3.423574 0.09852252 3323
ContextEffectfPublic                           -0.245300 0.05924298 3323
Agent_Action_levelfActive                      -0.222299 0.06104241 3323
AgentPresencefDisplayed                         0.012034 0.04296235 3323
ContextEffectfPublic:Agent_Action_levelfActive  0.219835 0.08638112 3323
                                                t-value p-value
(Intercept)                                    34.74915  0.0000
ContextEffectfPublic                           -4.14058  0.0000
Agent_Action_levelfActive                      -3.64172  0.0003
AgentPresencefDisplayed                         0.28011  0.7794
ContextEffectfPublic:Agent_Action_levelfActive  2.54494  0.0110
 Correlation: 
                                               (Intr) CntxEP Ag_A_A AgntPD
ContextEffectfPublic                           -0.294                     
Agent_Action_levelfActive                      -0.282  0.472              
AgentPresencefDisplayed                        -0.221  0.014 -0.001       
ContextEffectfPublic:Agent_Action_levelfActive  0.201 -0.688 -0.709 -0.003

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max 
-6.0949253 -0.4669407  0.1980209  0.6795859  2.0322987 

Number of Observations: 3803
Number of Groups: 
                                            ID 
                                            17 
PointingTaskStartingLocations_Building %in% ID 
                                           476 
Anova(AgentPresence)
Analysis of Deviance Table (Type II tests)

Response: log(AbsolutError_Building)
                                     Chisq Df Pr(>Chisq)    
ContextEffectf                     10.8551  1  0.0009852 ***
Agent_Action_levelf                 6.7974  1  0.0091292 ** 
AgentPresencef                      0.0786  1  0.7792503    
ContextEffectf:Agent_Action_levelf  6.4853  1  0.0108773 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwiset<- emmeans(TwofactorInteraction, pairwise ~ ContextEffectf*Agent_Action_levelf, type='response')
Pairwiset 
$emmeans
 ContextEffectf Agent_Action_levelf response   SE df lower.CL upper.CL
 Residential    Passive                 30.9 2.97 16     25.2     37.8
 Public         Passive                 24.1 2.33 16     19.7     29.6
 Residential    Active                  24.7 2.42 16     20.1     30.4
 Public         Active                  24.1 2.34 16     19.6     29.6

Degrees-of-freedom method: containment 
Confidence level used: 0.95 
Intervals are back-transformed from the log scale 

$contrasts
 contrast                                 ratio     SE   df null t.ratio
 Residential Passive / Public Passive     1.278 0.0757 3324    1   4.145
 Residential Passive / Residential Active 1.249 0.0762 3324    1   3.642
 Residential Passive / Public Active      1.281 0.0768 3324    1   4.138
 Public Passive / Residential Active      0.977 0.0604 3324    1  -0.376
 Public Passive / Public Active           1.002 0.0610 3324    1   0.039
 Residential Active / Public Active       1.026 0.0643 3324    1   0.409
 p.value
  0.0002
  0.0016
  0.0002
  0.9819
  1.0000
  0.9770

Degrees-of-freedom method: containment 
P value adjustment: tukey method for comparing a family of 4 estimates 
Tests are performed on the log scale 
ref_grid(TwofactorInteraction)
'emmGrid' object with variables:
    ContextEffectf = Residential, Public
    Agent_Action_levelf = Passive, Active
Transformation: "log" 
plot(Pairwiset[[2]])

anova(interceptOnlyt, IDrandomInterceptOnlyt, StartlocationsrandomInterceptt)
                               Model df      AIC      BIC    logLik   Test
interceptOnlyt                     1  2 8619.140 8631.627 -4307.570       
IDrandomInterceptOnlyt             2  3 7385.749 7404.479 -3689.874 1 vs 2
StartlocationsrandomInterceptt     3  5 8624.295 8655.512 -4307.147 2 vs 3
                                L.Ratio p-value
interceptOnlyt                                 
IDrandomInterceptOnlyt         1235.391  <.0001
StartlocationsrandomInterceptt 1234.546  <.0001
HumanAf$Agent_Category <- with(HumanAf, ave(seq_along(ID), ID, FUN = function(x) sample(c(rep('Action', ceiling(length(x)*0.6)), rep('Standing', length(x) - ceiling(length(x)*0.6))))))